Download Quiz 1 - Suraj @ LUMS

ROLL NO.
NAME
CS 537 – Neural Networks
Quiz 1 Solution
(Time limit: 10 minutes)
1. (6 points) Given the input x = [1, 2, 1, 2]T, weights w = [0.5, 0.5, 0.5, 0.5]T, and bias b
= 1, compute the outputs of the following neurons:
a. McCulloch-Pitts neuron
Incorporating the bias in the formulation:
x = [1, 1, 2, 1, 2]T; and w = [1, 0.5, 0.5, 0.5, 0.5]T
Output y = signum(wTx) = signum(4) = 1
(
b. A linear neuron (adder + linear activation function)
Output y = wTx = 4
c. A nonlinear neuron (adder + sigmoidal activation function with unity constants)
Output y = 1 / (1 + exp(-wTx)) = 1/(1+exp(-4)) = 0.9820
2. (2 points) Define machine learning in the context of a neural network. List the free
parameters that may be adapted during learning.
A neural network is said to learn if its free parameters are adapted in response to
experience in order to improve performance at learning an input-output mapping.
The free parameters can be:
 weights
 Activation function parameters
 Architectural parameters (e.g. number of layers, number of neurons per layer,
connectivity, etc)
3. (2 points) Given a linearly separable pattern, the perceptron will always find the same
unique hyperplane that discriminates the pattern. True or false, and explain briefly
why.
False. The exact hyperplane learned will depend on the initial weights, the sequence of
examples used for training, and the learning rate parameter. In general, if a pattern is
linearly separable there can be multiple (possibly infinite) hyperplanes that can correctly
distinguish between the two classes in the pattern.
CS 537 (Sp 06-07) – Dr. Asim Karim
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